Testing order/inequality Constrained Hypotheses in SEM
Testing order/inequality constrained Hypotheses in SEM
InformativeTesting(model = NULL, data, constraints = NULL,
R = 1000L, type = "bollen.stine",
return.LRT = TRUE,
double.bootstrap = "standard",
double.bootstrap.R = 249L,
double.bootstrap.alpha = 0.05,
parallel = c("no", "multicore", "snow"),
ncpus = 1L, cl = NULL, verbose = FALSE, ...)model |
Model syntax specifying the model. See |
data |
The data frame containing the observed variables being used to fit the model. |
constraints |
The imposed inequality constraints on the model. |
R |
Integer; number of bootstrap draws. The default value is set to 1000. |
type |
If |
return.LRT |
Logical; if |
double.bootstrap |
If |
double.bootstrap.R |
Integer; number of double bootstrap draws. The default value is set to 249. |
double.bootstrap.alpha |
The significance level to compute the adjusted
alpha based on the plugin p-values. Only used if |
parallel |
The type of parallel operation to be used (if any). If missing, the default is set "no". |
ncpus |
Integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs. |
cl |
An optional parallel or snow cluster for use if
|
verbose |
Logical; if |
... |
Other named arguments from the lavaan package which are passed to
the function. For example |
The following hypothesis tests are available:
Type A: Test H0: all restriktions with equalities ("=") active against HA: at least one inequality restriktion (">") strictly true.
Type B: Test H0: all restriktions with inequalities (">") (including some equalities ("=")) active against HA: at least one restriktion false (some equality restriktions may be maintained).
An object of class InformativeTesting for which a print and a plot method is available.
Leonard Vanbrabant lgf.vanbrabant@gmail.com
Van de Schoot, R., Hoijtink, H., & Dekovic, M. (2010). Testing inequality constrained hypotheses in SEM models. Structural Equation Modeling, 17, 443-463.
Van de Schoot, R., Strohmeier, D. (2011). Testing informative hypotheses in SEM increases power: An illustration contrasting classical. International Journal of Behavioral Development, 35, 180-190.
Silvapulle, M.J. and Sen, P.K. (2005). Constrained Statistical Inference. Wiley, New York.
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#########################
### real data example ###
#########################
# Multiple group path model for facial burns example.
# model syntax with starting values.
burns.model <- 'Selfesteem ~ Age + c(m1, f1)*TBSA + HADS +
start(-.10, -.20)*TBSA
HADS ~ Age + c(m2, f2)*TBSA + RUM +
start(.10, .20)*TBSA '
# constraints syntax
burns.constraints <- 'f2 > 0 ; m1 < 0
m2 > 0 ; f1 < 0
f2 > m2 ; f1 < m1'
# we only generate 2 bootstrap samples in this example; in practice
# you may wish to use a much higher number.
# the double bootstrap was switched off; in practice you probably
# want to set it to "standard".
example1 <- InformativeTesting(model = burns.model, data = FacialBurns,
R = 2, constraints = burns.constraints,
double.bootstrap = "no", group = "Sex")
example1
##########################
### artificial example ###
##########################
# Simple ANOVA model with 3 groups (N = 20 per group)
set.seed(1234)
Y <- cbind(c(rnorm(20,0,1), rnorm(20,0.5,1), rnorm(20,1,1)))
grp <- c(rep("1", 20), rep("2", 20), rep("3", 20))
Data <- data.frame(Y, grp)
#create model matrix
fit.lm <- lm(Y ~ grp, data = Data)
mfit <- fit.lm$model
mm <- model.matrix(mfit)
Y <- model.response(mfit)
X <- data.frame(mm[,2:3])
names(X) <- c("d1", "d2")
Data.new <- data.frame(Y, X)
# model
model <- 'Y ~ 1 + a1*d1 + a2*d2'
# fit without constraints
fit <- sem(model, data = Data.new)
# constraints syntax: mu1 < mu2 < mu3
constraints <- ' a1 > 0
a1 < a2 '
# we only generate 10 bootstrap samples in this example; in practice
# you may wish to use a much higher number, say > 1000. The double
# bootstrap is not necessary in case of an univariate ANOVA model.
example2 <- InformativeTesting(model = model, data = Data.new,
start = parTable(fit),
R = 10L, double.bootstrap = "no",
constraints = constraints)
example2
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